Daily
calibration of the FMT3 machine is required to compensate the effects of sample
preparation by different technicians and the ageing of the apparatus. As this
calibration involves the use of a limited stock of standard reference cotton,
the problem of replacing the standards arises when the latter are exhausted.
The standards are described by two values called PL and PH. This study covers
the stability of measurements in time, the incidence of two types of
calibration, the validity of the corrections made by calibration and the
evaluation of the PL and PH values of new standards by several technicians. The
USDA ICCS standards used are very homogeneous and supplied in 225-g rolls. The
differences between technicians and the heterogeneity of the rolls are taken
into account using a randomized experimental design and a linear model. It is
simple to use and requires little material and technician time. A daily
calibration by regression ensures a greater stability of FMT3 measurements and compensates
any technician effect.

KEYWORDS: maturity, FMT, calibration,
stability, bias

TITLE: Calibration, measurements stability
and replacement of standard cottons for an FMT318

INTRODUCTION

Fibre
maturity is an important feature as mature fibres
absorb dye better and are less prone to cause defects of various sorts in the
finished product. It is also important for breeders as it may show some defects
in the suitability of a variety to its environment. The commonest method of
measurement of micronaire (IM), fineness (H) and
maturity (MR) is based on the analysis of the resistance to air flow (PL and
PH) through cleaned cotton that a technician has placed in a short cylinder.
These measurements are defined by Montalvo et al.,
2002. Some models of the devices called “Fineness and Maturity Tester” (FMT) manufactured
by SDL-Atlas, Stockport, England, have long been used by
CIRAD for taking maturity characteristics into account in breeding programs.

Many
factors can disturb the measurement of maturity by compression in an air flow:
the condition of the apparatus and especially O-rings, various adjustments,
laboratory conditions or preparation and handling of the sample by the
technician (Montalvo et al., 2002). The apparatus
must therefore be calibrated satisfactorily to give readings that are stable in
time and identical from one machine to another. Reference or 'standard' cottons
are required for this.

To the best
of our knowledge, there is no recognised,
commercially available international standard with PL and PH values to
calibrate maturity evaluation apparatus (FMT® or Micromat®).
USDA proposes "ICCS USDA" cottons recognized for their good
homogeneity but that are only validated for micronaire
value IM (USDA, 1989). For this reason, the manufacturer SDL-Atlas supplies with each FMT3 apparatus two standard cottons of ICCS origin
and for which he has determined the PL and PH values. Each standard is taken
from a single bale weighing some 225 kg and is supplied in half-pound (225 g)
rolls. As PL and PH measurement is destructive, each calibration requires two
cotton test samples each weighing grams. The calibration 1 cotton runs out sooner or later and the parameters of the
calibration software must be adjusted to match new standards. Unfortunately,
the user cannot perform this operation. If a laboratory wishes to perform
routine calibration of the apparatus as often as necessary—in our opinion at
each change of technician and for each half-day of work—a substantial stock of
calibration standard material must be acquired on purchase of the apparatus. If
this has not been done, the laboratory faces the problem of performing calibration
using its own resources if it is desired to ensure long-term stability of the
maturity characteristics provided for clients. This problem encompasses the
homogeneity of standard cottons, allowance for the possible effect of
preparation by different technicians and finally the appropriateness and
accuracy of the corrections made.

The methods
that can be used to maintain a standard level by daily calibration and the way
in which we replace one standard by another when the first is practically
exhausted are described here. We check the appropriateness of calibration by
use of a correction factor or regression and evaluate new standards by allowing
for the differences between technicians and between rolls.

MATERIAL AND METHODS

Samples
were prepared using an SDL 099 fibre blender filled
with 10 to 12 grams raw fibre, opened by hand and
spread out in a layer about 40 cm by 10 cm.

All the
cottons were analysed using an FMT (model 3) maturity
tester (Shirley Developments, 1984) with no particular modifications. Air
pressure at input was maintained at the required 6 bars. Adjusted for 1 L and 4
L per minute, a rotameter float allows accurate
adjustment of the airflow used in each of the two depression measurements. This
flow was checked during every daily maintenance operation. The two cottons
supplied by the manufacturer are used to calibrate the apparatus before the
first readings are performed on the samples to be evaluated.

Variables subjected to calibration

Depressions
PL and PH are the subject of calibration. However, the FMT model 3 does not display
or transmit these variables directly, but rather micronaire
value IM, maturity ratio MR, mature fibre percentage
PM and fineness H (Lord & Heap, 1988):

These
equations are reversed to obtain the PL and PH values to be corrected, giving:

Cottons and technicians

Routine
calibration using old standards

This
routine calibration does not replace the obligatory calibration executed by the
software for the apparatus. However, this only takes place at each maintenance
operation—consisting mainly of inspecting the piston O-ring and changing it if
necessary. A cascade of two calibration operations is thus performed. The first
is planned in the operation of the machine, but with a limited stock of cotton,
and the second by us with a larger stock allowing everyday compensation for the
various interfering effects: ageing of O-rings and of the machine between two
maintenance operations, preparation and handling by the technician. Two methods
of calibration are compared: the correction factor (F) and linear regression
(R). The correction factor is estimated by the ratio of the reference
measurement to the measurement of the day on the same standards. With the other
procedure, the coefficients of the affine transformation are those of the
linear regression of the reference measurement to the measurement of the day.
We henceforth use the term 'observed result' for that given by the FMT3 machine
and its own calibration system, and 'corrected result' for that further
corrected by multiplicative correction (F) or by regression (R).

Three USDA
ICCS cottons, C38, L01 and M01, covering a broad range, are used as reference
and their PL and PH values form the level to be conserved. These are referred
to as theoretical values and were determined in late 1998 using FMT model 1
(Shirley Developments, 1977), with 3 technicians each performing 20
measurements (10 pairs of 2 fibre samples) weighing
4g ± 0.05g. All the cottons to be tested were prepared with the same blender
under the same conditions of temperature and relative humidity, 21°C and 65% RH (in conformity with the standard
ISO 139).

The values
of these three standards have been used on a routine basis since 2000 to calibrate
the FMT3 using our own procedure. Before each half-day of work, a technician performs
the cali 1 bration to be used for his measurements: he tests each of the 3
standards on two blended fibre samples weighing 3.8
to 4.2 g. The figures recorded on the FMT3 are entered in a SISTER® database (Gourlot & Giner, 1999) and
used to correct the measurements before they are delivered to the client. Set
up in May 2000 and maintained by the 9 technicians who have worked in the
laboratory, it contains determinations of PL and PH for 1445 triplets of the 3
cottons C38, L01 and M01. This record makes it possible to check the stability
of the raw measurements and, to a certain extent, the validity of the
corrections, either with a correction factor (F) or a linear regression (R).

Evaluation
of the new standards

We
conducted two experiments, each aimed at evaluating the PL and PH values of the
USDA ICCS standards: first cotton C39 and then cotton L02.

Each new
standard was from the same bale. It was evaluated by the 7 permanent
technicians at the laboratory. As it is available in several 225 g rolls, each
experiment combined several rolls and several technicians using a randomized
plan (Tables 1 and 2) in order to evaluate the variations between rolls, and
the second consisted of two separate replicates. Each replicate required no
more than half a day's work per technician. Little standard material was used:
the study required a total of 30 g per roll of cotton C39 and 60 g per roll of
L02 cotton. Each technician performed two measurements on each valid specimen
of between 3.8 and 4.2 g of fibre weighed accurately
on an Ohaus balance (accuracy 0.01 gram). Each
half-day was preceded by measurements on the usual C38, L01 and M01 standards
to calculate the correction factors for that half-day.

Statistical analysis

We first
sought to verify whether one or other of the calibration methods that we
propose is relevant. The values studied were the ‘observed' figures given by
the FMT3 with its own calibration. Then, to evaluate the PL and PH of the new
standards, we used the ‘corrected' figures, either by a correction factor (F)
or a regression (R).

Statistical
analyses and graphs were carried out using SAS/Stat and SAS/Graph software, version
9 (SAS Institute Inc., Cary, NC, USA),
namely the GLM and MIXED procedures, and the GLIMMIX macro.

Validity
of the correction factor

A correction factor is sufficient if all the variations
between cottons are proportional from one technician to another or, more
generally, from one half-day of work to another. In routine calibration
operations, this means that the regression equations should theoretically have
a nil intercept. In practice, the estimated intercepts that can be obtained at
each calibration operation, would then be distributed randomly around 0. This
hypothesis was tested by a Student test on the sample of intercepts obtained by
the calibrations performed by each technician.

n the
experiments on the new standards, with the same hypothesis of proportionality,
if iis the cotton index, j the
technician index and k the roll index, the expected measured value should
be: . On the logarithm scale, , the cotton and technician effects
are additive, in other words there is no interaction. Absence of interaction can
be tested with a generalised linear model (McCullagh and Nelder, 1983) in
which additivity is tested on the log scale but
errors are considered Gaussian in the original scale. To separate the random be
1 tween-roll variations from measurement
errors, the roll effect is added as an extra random term, making it a
generalized linear mixed model.

Validity of the linear regression

As
calibration regressions are calculated at 3 points, the linearity of the
relation is tested with verification that the residuals are nil on average for each cotton and more precisely for each cotton and each
technician. This was performed using the following linear model in which i, j and t are the indices for cotton,
technician and time, Yijtis the measured value and xi is the known value of cotton i:

The first
two terms are the regression equation varying according to the technician j and
time t and the last two are the supplementary effects of the cotton and
the interaction between cotton and technician; these two terms are nil if
linear calibration is valid. This test is used both on routine calibration
records and on experimental data, where index t is replaced by the replicate
number. In the first experiment with only one replicate, term dijdisappears as it is confounded with error. We also
compared the calibration values with the average values predicted by the
calibration equations in order to check the practical importance of deviations from
calibration.

Evaluation of new standards

We analyse the values corrected by the two calibration
methods; both are assumed to follow a linear mixed model, with roll effects and
technician replicate effects (two replicates per technician) being variance
components. The replicate effect encompasses the calibration error, only for
the new cotton that has not contributed to calibration. The new standards are evaluated
by their average values for all the technicians, each having equal weighting whatever
the number of rolls he or she processed. Standard errors are estimated
according to the variance components and experimental error. As replicates
exist only for the L02 new standard, standard errors are not calculated for the
C39 cotton.

RESULTS and DISCUSSION

Routine calibration of old standards

Stability
and variability in time before and after correction: graphic description

The
observed results presented in chronological order in Figures 1a and 2a display
fairly large dispersion of PL and PH, accentuated by rounding problems for PL.
Indeed, the values electronically transmitted by the FMT3 are rounded off to
one significant digit less than in the paper version. This results in
horizontal alignments of points and visibly has a marked impact on the accuracy
of the PL results. In contrast, PH was not visibly affected. A slight decrease in
PH was observed in the early months while the larger dispersion of PL results
meant that this could not be detected. The decrease in PH was confirmed by
linear regression according to the sequence number of the calibration operation
(Table 3).

The simple
correction factor stabilises the measurements
considerably (Figs. 1b and 2b). Further improvement can be achieved with
correction by regression (Figs. 1c and 2c).

Validity of correction by multiplicative
factor and by linear regression

If
correction by multiplicative factor were sufficient, the calibration lines
would theoretically pass via 0. It is seen in Table 4 that the average of the
intercepts is significantly different from zero for each technician. Student t
values are all significant with one exception. Calibration by correction
factor is therefore biased.

For
regression, the non-linearity 1 test described in the Material and
Methods section is also significant (Table 5): there is consistent departure
from linearity in all the regressions and the relation between observed values
and theoretical values is not linear in fact. Thus, in theory, neither
correction by multiplicative factor nor that by regression is satisfactory as
both generate biases in the average values with either method. However,
comparison of the theoretical values with the average values obtained shows
that these deviations are not of great practical importance (Table 6).

These
results that are stable in time at CIRAD do not reveal any noteworthy ageing of
the standard or of the machine and show that the calibration of a new standard
using old ones is legitimate.

Evaluation of new standards The validity of correction by
multiplicative factor was tested using the technician x cotton interaction on
the log scale (Table 7). It was rejected for cotton L02, but not for C39. The
linearity of the relation between theoretical value and observed value in the
known standard was tested by average deviation by cotton (cotton effect) and
the variations in these deviations according to technician (tech*cotton
interaction). The only significant figures were the average deviations by
cotton for the PL variable in the second experiment (Table 8). The bias of the
correction by multiplicative factor is more evident than that of the correction
by regression. With both calibration methods, the figures recorded as the new
reference for the laboratory are shown in Table 9. The figures corrected by
regression show more variability than those corrected by multiplicative factor.

DISCUSSION-CONCLUSION

Measurements
using FMT3 apparatus require calibration to cancel drift, reduce variability
and compensate the effect of the preparation and handling of the apparatus by
different technicians.

As calibration by regression or by
multiplicative factor gives stable measurements in time, changes of standard
can be envisaged with each new one calibrated with its predecessors. We needed
to develop a simple, rapid and effective technique to determine them with sufficient
accuracy.

The choice
between the two calibration methods is not made: while the linear regression method
is less biased than the constant factor method, its results are more variable
on the cotton that has not participated to the calibration. The compromise
between bias and variance has yet to be determined.

A shift,
even limited, is inevitable when a change is made as zero error cannot be
guaranteed at a change in standard. Inter-laboratory maturity tests are
therefore required so that laboratories can calibrate between each other and
avoid individual long-term drift.

Calibration
software should be modified so that standards can be changed, to avoid a
routine cascade of two calibration operations. Furthermore, it would be
preferable to base calibration on three cottons rather than two, with a warning
given in case of a sizeable deviation from linearity.

Although it
requires a temporary increase in daily calibration work, the overlapping of successive
standards would be another way of achieving a smooth transition from one standard
to another. It would also allow the empirical comparison of calibration
accuracy by constant factor and by regression.

The micromat operates usin1 g the same principle as the FMT3 and was tested in a fairly similar
experiment (Gawrysiak et al., 1998). The data should
be used in the same way to extend these results to other apparatus.

Figure 1:
Evolution in time of PL in standard cottons L01, C38 and M01: observed values
(a), values corrected by correction factor (b) and by regression (c). One different color for each technician.

Figure 2:
Evolution in time of PH in standard cottons L01, C38 and M01: observed values
(a), values corrected by correction factor (b) and by regression (c). One
different color for each technician. ACKNOWLEDGEMENT: The authors thank researchers
and technicians at the CIRAD cotton laboratory for FMT measurements and other contributions
to this paper. DISCLAIMER: Mention of a trademark, warranty, proprietary
product or vendor does not constitute a guarantee by CIRAD and does not imply
approval or recommendation of the product to the exclusion of others that may
be suitable. ABBREVIATION: Fiber Maturity Tester, model 3 (FMT3)